Properties

Label 4020.2.g.b
Level 4020
Weight 2
Character orbit 4020.g
Analytic conductor 32.100
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24q - 4q^{5} - 24q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 24q - 4q^{5} - 24q^{9} - 8q^{11} - 2q^{15} + 16q^{19} - 20q^{21} + 10q^{25} + 36q^{29} - 2q^{35} + 4q^{39} - 24q^{41} + 4q^{45} - 4q^{51} - 4q^{55} + 24q^{59} - 4q^{61} - 20q^{65} - 4q^{69} + 20q^{71} - 12q^{75} - 28q^{79} + 24q^{81} - 16q^{85} + 48q^{89} - 20q^{91} - 4q^{95} + 8q^{99} + O(q^{100}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1609.1 0 1.00000i 0 −2.22339 0.237781i 0 1.39060i 0 −1.00000 0
1609.2 0 1.00000i 0 −2.07549 0.832066i 0 0.944795i 0 −1.00000 0
1609.3 0 1.00000i 0 −1.71974 1.42915i 0 1.37984i 0 −1.00000 0
1609.4 0 1.00000i 0 −1.63494 + 1.52544i 0 3.48382i 0 −1.00000 0
1609.5 0 1.00000i 0 −1.47707 + 1.67877i 0 3.23400i 0 −1.00000 0
1609.6 0 1.00000i 0 −0.880059 2.05560i 0 1.30492i 0 −1.00000 0
1609.7 0 1.00000i 0 −0.131247 + 2.23221i 0 5.13753i 0 −1.00000 0
1609.8 0 1.00000i 0 0.853331 + 2.06684i 0 2.56410i 0 −1.00000 0
1609.9 0 1.00000i 0 1.39369 1.74860i 0 3.23145i 0 −1.00000 0
1609.10 0 1.00000i 0 1.45456 1.69831i 0 0.243187i 0 −1.00000 0
1609.11 0 1.00000i 0 2.21022 0.339036i 0 3.30262i 0 −1.00000 0
1609.12 0 1.00000i 0 2.23014 0.162710i 0 0.770377i 0 −1.00000 0
1609.13 0 1.00000i 0 −2.22339 + 0.237781i 0 1.39060i 0 −1.00000 0
1609.14 0 1.00000i 0 −2.07549 + 0.832066i 0 0.944795i 0 −1.00000 0
1609.15 0 1.00000i 0 −1.71974 + 1.42915i 0 1.37984i 0 −1.00000 0
1609.16 0 1.00000i 0 −1.63494 1.52544i 0 3.48382i 0 −1.00000 0
1609.17 0 1.00000i 0 −1.47707 1.67877i 0 3.23400i 0 −1.00000 0
1609.18 0 1.00000i 0 −0.880059 + 2.05560i 0 1.30492i 0 −1.00000 0
1609.19 0 1.00000i 0 −0.131247 2.23221i 0 5.13753i 0 −1.00000 0
1609.20 0 1.00000i 0 0.853331 2.06684i 0 2.56410i 0 −1.00000 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1609.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4020.2.g.b 24
5.b even 2 1 inner 4020.2.g.b 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4020.2.g.b 24 1.a even 1 1 trivial
4020.2.g.b 24 5.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{7}^{24} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(4020, [\chi])\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database